How many push ups at age 50 are usual?

200

one handed or two handed?

Come on now, one hand holds onto the dhringk.

I would say the typical 50 year old can't do a single pushup, but for a 50 year old who is regularly exercising and doesn't have any mobility issues, they should be able to do multiple sets of 10 pushups before approaching failure

Last year I (47 ) did a 100 push up a day challenge (30 days) and did keep it going after for some time. Built up from sets of 10 to 20 and still try keep it going .. it did help with bench press as well.

Also make sure you're not doing "Mickey dips"! Full plank, core tight, chest all the way to the floor and back up to full extension. Slow and measured is far better than a lot of crappy fast ones. It should take you 2 seconds to do one.

There are a lot of variations to the pushup.

Hand release pushups are used by the US military in strength tests and allow for more reps as there is a slight break in each movement.

Strict pushups are more fatiguing but people often cheat as they get tired and don't complete the full range of motion.

If you're trying to impress people, a single handstand pushup beats a hundred strict pushups

If you can do 20 pushups you'd be better off progressing to sets of 10 weighted pushups, or deficit pushups or (if you're a bit sadistic) ring pushups, than increasing your reps to strict 30 pushups

(If only because higher reps of bodyweight exercises are more boring and time consuming for not much strength gain)

If you want to just work your chest you don’t need to go down too low. Just making a 90 degree angle with your elbow is fine for a good chest push up. If you could do 50 push-ups like that it is quite good.

Would say that a good general fitness test would be push-ups, pull-ups, burpees and 5k time. If you can do these four things regularly and get decent strength/fitness in each then you would have a good fitness base at any age! Something like at least 50 press-ups without stopping; 40 burpees, 15 pull-ups and under 25 mins for a 5k (not one exercise after the other, just in general).

Are push ups any good for reducing breast size? I'm 52 and not fit or strong

This is true.
Increasing the variation difficulty and adding extra weight in a backpack or vest once you’ve mastered the form of that variation is the key.
Ring push ups with elevated feet (on a bench) with a 10Kg vest and you would be lucky to get 5 even though you might be able to lash out 20 bodyweight normal push ups.